The sun actually moves itself, Celestia just has to make sure it’s going on course every once in a while. While she can move it, she technically doesn’t have to every morning. In other words, it’s all for show.
Bonus: Actually, she didn’t know she didn’t have to move it until one morning where she accidentally slept in after a long night of negotiations. After testing it out for a few nights, making sure Luna wasn’t interfering, she discovered the truth.
Prince Blueblood has a knack for knocking up mares across Equestria, and getting away with it. Luna wants the royal palace to stop covering for him, but Celestia doesn’t want any royal scandals breaking out.